Any shortcuts for this problem??

[beater]

The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?


I. 3
II. 7
III. 12


A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

[cramya]

I cant think of a shorcut other than subsituting numbers and calculating the mean and median.

I got D)I and III

[stop@800]

There are other methods but those are not turning out to be shortcuts.

Best would be substitution.

[Saffa]

The median can only be an integer or halfway between integers. Because there are 6 numbers and the first 5 is already divisible by 6, the other number must be a multiple of 3.

THIS DOES NOT SOLVE IT THOUGH

It just help you eliminate 1 quickly